Making the wave observable in the double-slit experiment

[Quantum Waver]

You can see that claim A and B are closely related, but not identical. I have seen Sean Carroll discuss A. I have seen him contrast it with C. I have not seen him discuss B.

I'm fairly confident Carroll disagrees with B on the grounds that classical stuff like measuring devices emerge from the quantum, so it shouldn't be part of the QM formalism, if QM is a fundamental theory. Instead, measurement and experimental setups should all be understood in a quantum pseudo-classical manner. At least as I understand what the implication of MWI is for the macroscopic.

It turns the CI and instrumentalism on it's head, focusing on the quantum instead of the classical. Whereas Bohr (at least) thought classical concepts were essential for making scientific statements. Maybe modern instrumentalists have a more nuanced take about the quantum/classical divide.

 

[Morbert]

I'm fairly confident Carroll disagrees with B on the grounds that classical stuff like measuring devices emerge from the quantum, so it shouldn't be part of the QM formalism, if QM is a fundamental theory.

Asher Peres addresses this in the same book.

There should be no misunderstanding. Bohr never claimed that different physical laws applied to the microscopic and macroscopic systems. He only insisted on the necessity of using different modes of description for the two classes of objects. It must be recognized that this approach is not entirely satisfactory. [...] This raises a thorny issue. We may wish to extend the microscopic (supposedly exact) theory to objects of intermediate size. [...] Ultimately we must explain how a very large number of microscopic entities, described by an utterly complicated vector in many dimensions, combine to form a macroscopic object endowed with classical properties.
[...]
The hallmark of a measuring instrument, which distinguishes it from other physical objects, is this ambivalence: it must be treated as a quantum system while it interacts with the measured object, and as a classical system once the measurement is over. How can we "dequantize" the apparatus? Can this "dequantization" be done consistently?

He goes on to sketch out this dequantization: A quantum system $S$ coupled to an apparatus $A$ gives us a density matrix $\rho_{S+A}$ which gives us a reduced density matrix $\rho_A$ which gives us a Wigner function $W_A(\mathbf{q},\mathbf{p})$, which gives us a fuzzy Wigner function. which gives us a Liouville density $f_A(\mathbf{q},\mathbf{p})$ which gives us a probability distribution for the final classical state of the apparatus.

In short, instrumentalism does not demote quantum theory to something that only applies to a patch of the universe. It is universal and exact and fundamental. Classical physics only plays a role as a mode of description that we deploy to get our probabilities for the data we register, and an understanding continuous with Bohr, but nevertheless post-Bohr, consistently relates the two.

 

[Morbert]

So Peres formulation of instrumentalism is still realist about the microphysical.

Yes, where he departs from realism is the properties of the microphysical measured by our instruments, and characterised by quantum mechanics. A quantum system to him is "an equivalence class of preparations" and is not real, even if the microscopic world is.

 

[gentzen]

If we look through his writings, we will probably find-out his thoughts and positions regarding "anti-realism" and "Copenhagen" (or we could ask him, if we really want to know). Regarding "instrumentalism," I guess Sean was careful not to say too much about it,

I did that search now, and it seems I was right that it is easy to find material online where Sean writes/talks about "anti-realism" or "Copenhagen" (although never at the same time about both), but hard to find him talking about "instrumentalism". I didn't have enough patience to understand in detail what he writes about anti-realism, but his position regarding Copenhagen is easy to understand, therefore I quote it here:

https://www.preposterousuniverse.com/blog/2013/01/17/the-most-embarrassing-graph-in-modern-physics/

I’ll go out on a limb to suggest that the results of this poll should be very embarrassing to physicists. Not, I hasten to add, because Copenhagen came in first, although that’s also a perspective I might want to defend (I think Copenhagen is completely ill-defined, and shouldn’t be the favorite anything of any thoughtful person). The embarrassing thing is that we don’t have agreement.
...
I’m sitting in a bistro at the University of Nottingham, where I gave a talk yesterday about quantum mechanics. I put it this way: here in 2013, we don’t really know whether objective “wave function collapse” is part of reality (as the poll above demonstrates). We also don’t know whether, for example, supersymmetry is part of reality. Wave function collapse has been a looming problem for much longer, and is of much wider applicability, than the existence of supersymmetry. Yet the effort that is put into investigating the two questions is extremely disproportionate.

https://www.preposterousuniverse.com/eternitytohere/quantum/

The Copenhagen interpretation of quantum mechanics is as easy to state as it is hard to swallow: when a quantum system is subjected to a measurement, its wave function collapses. That is, the wave function goes instantaneously from describing a superposition of various possible observational outcomes to a completely different wave function, one that assigns 100 percent probability to the outcome that was actually measured, and 0 percent to anything else. That kind of wave function, concentrated entirely on a single possible observational outcome, is known as an “eigenstate.” Once the system is in that eigenstate, you can keep making the same kind of observation, and you’ll keep getting the same answer (unless something kicks the system out of the eigenstate into another superposition). We can’t say with certainty which eigenstate the system will fall into when an observation is made; it’s an inherently stochastic process, and the best we can do is assign a probability to different outcomes.

He says

The most important point is that the underlying goal of science is not simply making predictions — it’s developing an understanding of ... the natural world

Which sounds like shut up and calculate: "Who cares how the world works. All that matters is calculating predictions." At best it is an uncharitable reduction. The instrumentalist approach as exemplified by authors like Asher Peres ...

My reply are the "..." above. Hope it demonstrates how we both read our own "interpretation" of Sean into his writings. But at least his position regarding Copenhagen quoted above is pretty straightforward and "immune" to different interpretations. That was my main reason to write this comment, and I will stop here.

 

[Quantum Waver]

Going back to the first video, I have a naive question about measurement. Both the screen and the smoke act as measurements, but they don't destroy interference, even if one photon were emitted at a time. So why does using a detector cause decoherence? Is it because it's detecting photons in one specific location, or is it because the detector is a complex macroscopic object?

Debates around measurement, collapse and decoherence seem to confuse the issue as to exactly when and why a measurement destroys the interference pattern. If the environment is causing decoherence, then why does the smoke and screen still allow for an interference pattern?

 

[Morbert]

Going back to the first video, I have a naive question about measurement. Both the screen and the smoke act as measurements, but they don't destroy interference, even if one photon were emitted at a time. So why does using a detector cause decoherence? Is it because it's detecting photons in one specific location, or is it because the detector is a complex macroscopic object?

Debates around measurement, collapse and decoherence seem to confuse the issue as to exactly when and why a measurement destroys the interference pattern. If the environment is causing decoherence, then why does the smoke and screen still allow for an interference pattern?

The smoke doesn't detect which slit the photon went through, which is what would destroy interference.

 

[Quantum Waver]

The smoke doesn't detect which slit the photon went through, which is what would destroy interference.

But if you just block off one of the slits, you get a single slit diffraction pattern. So would attaching a tube to the one open slit long enough to fill just the tube with smoke count as a detector?

 

[Morbert]

But if you just block off one of the slits, you get a single slit diffraction pattern. So would attaching a tube to the one open slit long enough to fill just the tube with smoke count as a detector?

The smoke isn't analogous to the detector behind the slits in the conventional double-slit experiment. A photon detected by smoke is destroyed. As such, it is more like the 2D detector screen in the conventional experiment. It registers whether or not there is an interference pattern. It does not register which slit the photons went through.

 

[PeterDonis]

I don't believe you can call it "entanglement", as in the usual meaning

But that's what the equations say. It's not just pulled out of thin air, it is literally what the math (without collapse) tells you happens during any interaction. Measurement is just a type of interaction.

If that were true, monogamy of entanglement would be violated

No, it wouldn't. The entanglement created by an interaction does not have to be maximal. Non-maximal entanglements can be spread out among an arbitrary number of degrees of freedom. That is the basis of decoherence theory.

 

[PeterDonis]

What Wallace argues is that branches/worlds are emergent phenomena from the components of entangled environments

Yes, I understand all this. I'm just pointing out that it is not how any physicists, including MWI proponents, talk about ordinary entangled systems. The "branches/worlds" talk is an extra element that has to be added in for some particular kinds of entanglements. The only basis in the math for making any such distinction is decoherence, but decoherence is not a sharp distinction, it's gradual, whereas the "branches/worlds" distinction is sharp--either the individual terms in an entangled state represent "branches/worlds" or they don't. But nobody, AFAIK, has given any kind of criterion for where the boundary is--where "branches/worlds" come into being.

 

[PeterDonis]

There is an interaction I presume between each possible individual MWI branch when an observed particle interacts with the observer environment.

No. There is no interaction between branches. The branches are the outcome of the interaction.

For example, consider a single electron passing through a Stern-Gerlach device. Say the electron starts in the z-spin up state, and the Stern-Gerlach device is oriented in the x direction. Then the state before the interaction is

$$
\ket{z+} \ket{\text{input beam}}
$$

and the state after the interaction is

$$
\frac{1}{\sqrt{2}} \left( \ket{x+} \ket{\text{x-spin up beam}} + \ket{x-} \ket{\text{x-spin down beam}} \right)
$$

The former state is a product state, but the latter state is an entangled state; the entanglement is produced by the interaction between the electron and the Stern-Gerlach apparatus.

This interaction by itself does not necessarily produce decoherence, since the beams can in principle be recombined; to complete a spin measurement one needs to put detectors in each output beam and observe which one fires. But the entangled state produced by that further interaction looks simliar to the above, just with an additional ket for the detector system.

I don't know what you would say is the entangled attribute/observable though.

In the Stern-Gerlach case, the entanglement is between the spin and the momentum of the electron. The specific degrees of freedom that are entangled will depend on the particular interaction.

Or what the conserved quantity is.

I'm not sure why a conserved quantity would be relevant.

 

[vanhees71]

But that's what the equations say. It's not just pulled out of thin air, it is literally what the math (without collapse) tells you happens during any interaction. Measurement is just a type of interaction.No, it wouldn't. The entanglement created by an interaction does not have to be maximal. Non-maximal entanglements can be spread out among an arbitrary number of degrees of freedom. That is the basis of decoherence theory.

That's of course right: In an ideal von Neumann filter measurement the measurement appartus's "pointer state" gets maximally entangled with the system's state. That's the definition of a von Neumann filter measurement.

Take the ideal Stern Gerlach experiment: You measure a spin component by letting the Ag atoms through an appropriate magnetic field (large constant part in direction of the spin component to be measured and some inhomogeneous part) to entangle the spin component with the position of the particle. Then measurement of the position is 100% correlated with measuring the spin component.

 

[vanhees71]

This interaction by itself does not necessarily produce decoherence, since the beams can in principle be recombined; to complete a spin measurement one needs to put detectors in each output beam and observe which one fires. But the entangled state produced by that further interaction looks simliar to the above, just with an additional ket for the detector system.

Indeed, the time evolution of a closed system is always unitary and (in principle) reversible. Decoherence occurs when looking at a sub system of a larger system. The effective description of the state evolution of the subsystem, i.e., its reduced statistical operator is described in terms of some non-unitary master equation, which involves decoherence through the interaction of the "system" with "the environment".

By chance, there's just a nice Nature paper about the issue, how the 2nd law of thermodynamics (H-theorem) for subsystems is compatible with the unitary evolution of the closed system:

https://doi.org/10.1038/s41467-023-38413-9 (open access!)

 

[kered rettop]

TL;DR Summary: Physicist becomes convinced Schrödinger's equation describes real waves, because they can be made visible in the double-slit experiment using a laser and smoke machine.

I don't see how the smoke makes the wave visible. Each photon is scattered by the smoke at a different point, so it's equivalent to having the screen at that point. You are not watching the evolution of a single photon's wave function, you're just seeing its final state (where it's scattered). You can assume that they all behave the same way, but that just begs the question.

 

[vanhees71]

Obviously Youtube has not only very good explanations of QT. Very likely a good textbook is the better choice for learning it!

 

[kered rettop]

Going back to the first video, I have a naive question about measurement. Both the screen and the smoke act as measurements, but they don't destroy interference, even if one photon were emitted at a time. So why does using a detector cause decoherence? Is it because it's detecting photons in one specific location, or is it because the detector is a complex macroscopic object?

Debates around measurement, collapse and decoherence seem to confuse the issue as to exactly when and why a measurement destroys the interference pattern. If the environment is causing decoherence, then why does the smoke and screen still allow for an interference pattern?

Yes they do destroy interference. If the photon is scattered by the smoke or reflected off the screen, you can't coax interference out of it. The unscattered photons carry on interfering.

The environment only causes decoherence if the particle interacts with it. It can't do anything just by being.